When I made the move from 4th grade and Special Education to kindergarten two years ago, it was clear to me that I had the important job of building a strong foundation for my students. When I taught older students, I could see gaps in their understanding of basic principles in math and reading. Their lack of strong phonemic awareness plagued them even in 4th grade. Their shaky understanding of number sense made fractions and multiplication that much more challenging.
Kindergarten, clearly, is a place where students learn vital life skills. They learn to share, they learn to solve problems, they learn to be a part of a community. Play is a welcome platform to build skills they need for reading and math when they get older. Just like we know phonemic awareness sets the building blocks for reading, number sense does the same for mathematics.
This year, we have taken a leap in our math instruction. What used to be a lot of worksheet based instruction, mostly teacher led, is now inspired by cognitively guided instruction. Using theories aligned with this form of instruction we give students more opportunities to use what comes naturally to them – play and exploration – to build their number sense. Our math work comes in three parts: morning meeting, number talks, and a formal math block.
Every day starts with a morning meeting block that includes a lot of literacy and community building. This is also the time when we use our 100s chart to explore counting, the concepts of more and less, and forming of numerals. For the first 100 days of school, we add a new number to our chart. Students notice patterns as we build the chart and make predictions about what number might come next or even 10 after. We count by ones and start counting by 10s. Once the chart is full, we start manipulating it. We play, “Mystery Number’ in which students guess a mystery number based on clues. “My number is one more than 5. What is my number?” or “My number is an even number. What is my number?” This quick, less than 5 minute routine, familiarizes students with the first 100 numbers. We get used to reading them, we use them to help us write them, and we notice patterns.
Number talks are a short mental math activity. When I used these in 4th grade, they took about 10 minutes. In kindergarten, the routine lasts around 5. The structure starts with presenting student a short math problem. Students solve the problem mentally – no manipulatives and no paper. Students then share their answers and in older grades, these are recorded by the teacher. Other students can agree, disagree, add on, etc. In kindergarten, we first present images of dots in different arrangements. This helps students learn to subitize – or to automatically see a total amount. You probably do this when you see the arrangements on dice. When you roll a 5, you don’t have to count, you just know it is 5. Subitizing is an important skill that builds on number sense. We move from subitization with dots to subitization within 10 frames which will lay the groundwork for addition and subtraction.
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During our math block, from the very beginning of the year, we present students with story problems. Students are invited to solve the problems in any way they would like. They can use blocks, cubes, other math tools and manipulatives. They can also use materials to draw their answer and write numbers, sometimes on paper, sometimes on white boards. After students solve the problem in their own way, they come together to share their work. Students learn from each other and get to play and manipulate different ideas of numbers in ways that make sense to them. They grow their understanding by hearing other students ideas. Our role as teachers is to help students synthesize the new information they hear and identify patterns. We learn that when groups are joined together they get bigger. Eventually, after lots of repeated practice, we learn that we call this addition. We are just getting to this understanding now, in March, and we have been doing this work since September. Since moving away from worksheets, students are much more engaged in the thinking that is required in math.
With the implementation of these three mathematical practices, I have seen my students take ownership of their math in a whole new way. They are able to show their thinking and share it with others. This is our first year implementing the new system and there are certainly areas in which we will grow in the years to come. But these changes have definitely helped me, and more importantly my students, make sense of number sense. I am excited to hear from their 4th grade teachers a few years down the line.